Tagged Questions

Why is Brownian motion required to be merely almost surely continuous instead of continuous?
For example, this is stated as condition 2 in this article in section 1, Characterizations of the Wiener ...

If we have the density function
$$f_{Y}(y,t)=\frac{1}{y \sqrt {2\pi\sigma^2t}}exp(-\frac{(ln \ y - \mu t)^2}{2\sigma^2t})$$
Then the mean of $Y(t)=e^{X(t)}$ conditional on $Y(0)=y_0$ is found to be
...

I was thinking of using Geometric Brownian Motion to forecast future prices of timber (say one variable, the stumpage price of sawtimber).
I tested the time series with Augmented Dickey-Fuller test ...

I am trying to understand how the first passage time density of Brownian motion with drift is modified by the presence of waiting times that are distributed as a power law
In other words, what is the ...